%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU760^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:33:18 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU760^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:23:03 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.32 % (850949)Will run a generic schedule for satisfiability detection.
% 0.22/0.32 % (850955)% WARNING: option uhcvi not known.
% 0.22/0.32 % (850955)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1499829707:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.32 % (850956)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2837561752:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.32 % (850955)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.32 % (850955)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.32 % (850957)dis+10_1_sil=32000:sp=arity:random_seed=191896874:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.32 % (850954)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2290744249_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.32 % Exception at run slice level
% 0.22/0.32 % (850960)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=437554354:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.32 % (850959)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4000431236:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.32 % (850958)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1013024405:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.32 % (850958)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.32 % (850955) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-850949-850955"...
% 0.22/0.32 % (850955)...printing done.
% 0.22/0.32 % (850955)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% 0.22/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.32 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.32 thf(func_def_1, type, powerset: ($i > $i)).
% 0.22/0.32 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.22/0.32 thf(func_def_3, type, subsetI1: $o).
% 0.22/0.32 thf(func_def_5, type, subsetE: $o).
% 0.22/0.32 thf(func_def_6, type, binintersect: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_7, type, binintersectER: $o).
% 0.22/0.32 thf(func_def_8, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.32 thf(func_def_9, type, vIMP: ($o > $o > $o)).
% 0.22/0.32 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.32 thf(func_def_20, type, vNOT: ($o > $o)).
% 0.22/0.32 thf(func_def_21, type, sK4: ($i > $i > $i)).
% 0.22/0.32 thf(f1,axiom,(
% 0.22/0.32 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.22/0.32 thf(f2,axiom,(
% 0.22/0.32 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.22/0.32 thf(f3,axiom,(
% 0.22/0.32 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)).
% 0.22/0.32 thf(f4,conjecture,(
% 0.22/0.32 subsetI1 => (subsetE => (binintersectER => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3)))))))),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule2)).
% 0.22/0.32 thf(f5,negated_conjecture,(
% 0.22/0.32 ~(subsetI1 => (subsetE => (binintersectER => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))))),
% 0.22/0.32 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.32 thf(f6,plain,(
% 0.22/0.32 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.22/0.32 inference(rectify,[],[f1])).
% 0.22/0.32 thf(f7,plain,(
% 0.22/0.32 (subsetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 0.22/0.32 inference(fool_elimination,[],[f6])).
% 0.22/0.32 thf(f8,plain,(
% 0.22/0.32 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.22/0.32 inference(rectify,[],[f2])).
% 0.22/0.32 thf(f9,plain,(
% 0.22/0.32 (subsetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))))))),
% 0.22/0.32 inference(fool_elimination,[],[f8])).
% 0.22/0.32 thf(f10,plain,(
% 0.22/0.32 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 0.22/0.32 inference(rectify,[],[f3])).
% 0.22/0.32 thf(f11,plain,(
% 0.22/0.32 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))))),
% 0.22/0.32 inference(fool_elimination,[],[f10])).
% 0.22/0.32 thf(f12,plain,(
% 0.22/0.32 ~(subsetI1 => (subsetE => (binintersectER => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))))),
% 0.22/0.32 inference(rectify,[],[f5])).
% 0.22/0.32 thf(f13,plain,(
% 0.22/0.32 ~((subsetI1 = $true) => ((subsetE = $true) => ((binintersectER = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => ! [X3 : $i] : ((((in @ X3 @ (powerset @ X0))) = $true) => ((((subset @ X2 @ X3)) = $true) => (((subset @ (binintersect @ X1 @ X2) @ X3)) = $true))))))))),
% 0.22/0.32 inference(fool_elimination,[],[f12])).
% 0.22/0.32 thf(f14,plain,(
% 0.22/0.32 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((((subset @ (binintersect @ X1 @ X2) @ X3)) != $true) & (((subset @ X2 @ X3)) = $true)) & (((in @ X3 @ (powerset @ X0))) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (binintersectER = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 0.22/0.32 inference(ennf_transformation,[],[f13])).
% 0.22/0.32 thf(f15,plain,(
% 0.22/0.32 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((subset @ (binintersect @ X1 @ X2) @ X3)) != $true) & (((subset @ X2 @ X3)) = $true) & (((in @ X3 @ (powerset @ X0))) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (binintersectER = $true) & (subsetE = $true) & (subsetI1 = $true)),
% 0.22/0.32 inference(flattening,[],[f14])).
% 0.22/0.32 thf(f16,plain,(
% 0.22/0.32 (((($true != ((subset @ (binintersect @ sK1 @ sK2) @ sK3))) & ($true = ((subset @ sK2 @ sK3))) & ($true = ((in @ sK3 @ (powerset @ sK0))))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (binintersectER = $true) & (subsetE = $true) & (subsetI1 = $true)),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15])).
% 0.22/0.32 thf(f17,plain,(
% 0.22/0.32 (subsetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 0.22/0.32 inference(cnf_transformation,[],[f7])).
% 0.22/0.32 thf(f18,plain,(
% 0.22/0.32 (subsetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))))))),
% 0.22/0.32 inference(cnf_transformation,[],[f9])).
% 0.22/0.32 thf(f19,plain,(
% 0.22/0.32 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))))),
% 0.22/0.32 inference(cnf_transformation,[],[f11])).
% 0.22/0.32 thf(f20,plain,(
% 0.22/0.32 (subsetI1 = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f16])).
% 0.22/0.32 thf(f21,plain,(
% 0.22/0.32 (subsetE = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f16])).
% 0.22/0.32 thf(f22,plain,(
% 0.22/0.32 (binintersectER = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f16])).
% 0.22/0.32 thf(f26,plain,(
% 0.22/0.32 ($true = ((subset @ sK2 @ sK3)))),
% 0.22/0.32 inference(cnf_transformation,[],[f16])).
% 0.22/0.32 thf(f27,plain,(
% 0.22/0.32 ($true != ((subset @ (binintersect @ sK1 @ sK2) @ sK3)))),
% 0.22/0.32 inference(cnf_transformation,[],[f16])).
% 0.22/0.32 thf(f29,definition,(
% 0.22/0.32 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.32 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.32 thf(f30,plain,(
% 0.22/0.32 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))) = $true)),
% 0.22/0.32 inference(definition_unfolding,[],[f17,f20])).
% 0.22/0.32 thf(f31,plain,(
% 0.22/0.32 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))))) = $true)),
% 0.22/0.32 inference(definition_unfolding,[],[f18,f21])).
% 0.22/0.32 thf(f32,plain,(
% 0.22/0.32 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))) = $true)),
% 0.22/0.32 inference(definition_unfolding,[],[f19,f22])).
% 0.22/0.32 thf(f33,plain,(
% 0.22/0.32 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))) @ X1)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f32])).
% 0.22/0.32 thf(f34,plain,(
% 0.22/0.32 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y0))))))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f33])).
% 0.22/0.32 thf(f35,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y0))))) @ X2)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f34])).
% 0.22/0.32 thf(f36,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ X2))))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f35])).
% 0.22/0.32 thf(f37,plain,(
% 0.22/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ X2))) @ X3)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f36])).
% 0.22/0.32 thf(f38,plain,(
% 0.22/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (binintersect @ X3 @ X2)) => (in @ X1 @ X2))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f37])).
% 0.22/0.32 thf(f39,plain,(
% 0.22/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (binintersect @ X3 @ X2)))) | ($true = ((in @ X1 @ X2)))) )),
% 0.22/0.32 inference(imp_proxy_clausification,[],[f38])).
% 0.22/0.32 thf(f40,plain,(
% 0.22/0.32 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))) @ X1)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f31])).
% 0.22/0.32 thf(f41,plain,(
% 0.22/0.32 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((in @ X1 @ Y1) => (in @ X1 @ Y0)))))))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f40])).
% 0.22/0.32 thf(f42,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((in @ X1 @ Y1) => (in @ X1 @ Y0)))))) @ X2)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f41])).
% 0.22/0.32 thf(f43,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X2) => ((in @ X1 @ Y0) => (in @ X1 @ X2)))))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f42])).
% 0.22/0.32 thf(f44,plain,(
% 0.22/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((subset @ Y0 @ X2) => ((in @ X1 @ Y0) => (in @ X1 @ X2)))) @ X3)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f43])).
% 0.22/0.32 thf(f45,plain,(
% 0.22/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((subset @ X3 @ X2) => ((in @ X1 @ X3) => (in @ X1 @ X2)))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f44])).
% 0.22/0.32 thf(f46,plain,(
% 0.22/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X3 @ X2))) | ($true = (((in @ X1 @ X3) => (in @ X1 @ X2))))) )),
% 0.22/0.32 inference(imp_proxy_clausification,[],[f45])).
% 0.22/0.32 thf(f47,plain,(
% 0.22/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X3 @ X2))) | ($false = ((in @ X1 @ X3))) | ($true = ((in @ X1 @ X2)))) )),
% 0.22/0.32 inference(imp_proxy_clausification,[],[f46])).
% 0.22/0.32 thf(f48,plain,(
% 0.22/0.32 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))) @ X1)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f30])).
% 0.22/0.32 thf(f49,plain,(
% 0.22/0.32 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f48])).
% 0.22/0.32 thf(f50,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))) @ X2)))) )),
% 0.22/0.32 inference(pi_proxy_clausification,[],[f49])).
% 0.22/0.32 thf(f51,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (subset @ X2 @ X1))))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f50])).
% 0.22/0.32 thf(f52,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.22/0.32 inference(imp_proxy_clausification,[],[f51])).
% 0.22/0.32 thf(f53,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK4 @ X1 @ X2)))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.22/0.32 inference(sigma_proxy_clausification,[],[f52])).
% 0.22/0.32 thf(f54,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ (sK4 @ X1 @ X2) @ X2) => (in @ (sK4 @ X1 @ X2) @ X1)))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.22/0.32 inference(beta-eta_normalization,[],[f53])).
% 0.22/0.32 thf(f55,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK4 @ X1 @ X2) @ X1))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.22/0.32 inference(imp_proxy_clausification,[],[f54])).
% 0.22/0.32 thf(f56,plain,(
% 0.22/0.32 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X1 @ X2) @ X2))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.22/0.32 inference(imp_proxy_clausification,[],[f54])).
% 0.22/0.32 thf(f61,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ X0 @ sK2))) | ($true = ((in @ X0 @ sK3)))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f26,f47])).
% 0.22/0.32 thf(f66,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK3))) | ($false = ((in @ X0 @ sK2)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f61])).
% 0.22/0.32 thf(f77,plain,(
% 0.22/0.32 ($true != $true) | (((subset @ (binintersect @ sK1 @ sK2) @ sK3)) = $false)),
% 0.22/0.32 inference(constrained_superposition,[],[f27,f29])).
% 0.22/0.32 thf(f85,plain,(
% 0.22/0.32 (((subset @ (binintersect @ sK1 @ sK2) @ sK3)) = $false)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f77])).
% 0.22/0.32 thf(f97,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ (sK4 @ sK3 @ X0) @ sK2))) | ($true = ((subset @ X0 @ sK3)))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f66,f55])).
% 0.22/0.32 thf(f98,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($false = ((in @ (sK4 @ sK3 @ X0) @ sK2))) | ($true = ((subset @ X0 @ sK3)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f97])).
% 0.22/0.32 thf(f108,plain,(
% 0.22/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($true = ((in @ (sK4 @ X0 @ (binintersect @ X1 @ X2)) @ X2))) | ($true = ((subset @ (binintersect @ X1 @ X2) @ X0)))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f39,f56])).
% 0.22/0.32 thf(f109,plain,(
% 0.22/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X0 @ (binintersect @ X1 @ X2)) @ X2))) | ($true = ((subset @ (binintersect @ X1 @ X2) @ X0)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f108])).
% 0.22/0.32 thf(f598,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($true = $false) | ($true = ((subset @ (binintersect @ X0 @ sK2) @ sK3))) | ($true = ((subset @ (binintersect @ X0 @ sK2) @ sK3)))) )),
% 0.22/0.32 inference(constrained_superposition,[],[f98,f109])).
% 0.22/0.32 thf(f605,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($true = $false) | ($true = ((subset @ (binintersect @ X0 @ sK2) @ sK3)))) )),
% 0.22/0.32 inference(duplicate_literal_removal,[],[f598])).
% 0.22/0.32 thf(f606,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($true = ((subset @ (binintersect @ X0 @ sK2) @ sK3)))) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f605])).
% 0.22/0.32 thf(f640,plain,(
% 0.22/0.32 ($true = $false)),
% 0.22/0.32 inference(constrained_superposition,[],[f85,f606])).
% 0.22/0.32 thf(f641,plain,(
% 0.22/0.32 $false),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f640])).
% 0.22/0.32 % SZS output end Proof for theBenchmark
% 0.22/0.32 % (850955)------------------------------
% 0.22/0.32 % (850955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (850955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (850955)CaDiCaL version: 2.1.3
% 0.22/0.32 % (850955)Termination reason: Refutation
% 0.22/0.32 % (850955)Time elapsed: 0.031 s
% 0.22/0.32 % (850955)Peak memory usage: 12 MB
% 0.22/0.32 % (850955)Instructions burned: 61 (million)
% 0.22/0.32 % (850949)Success in time 0.073 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------